7 A company's total profit from manufacturing and selling x units of their model product is given by P'(x)=-0.02x2+300x-200000(0≤x≤20,000) How many units of the products must the company produce to maximize their profits? (10%)

(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)

7 A company's total profit from manufacturing and selling x units of their model product is given by P'(x)=-0.02x²+300x-200000(0≤x≤20,000)
How many units of the products must the company produce to maximize their profits? (10%)

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